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Another knowledge packedPre-Calculus experience!

3.4 Exponential and Logarithmic Equations

p251 #13-25eoo, 31-43eoo,53-69eoo, 71-111eoo

Homework for section 3.4

Solving simple equations…

OriginalEquatio

n2 32x

Rewritten

EquationSolutio

n 52 2x 5x

ln ln 3 0x ln ln 3x 3x

1 93x

23 3x 2x

7xe ln ln 7xe ln 7x ln 3x ln 3xe e 3x e

10log 1x 10log 110 10x 1 110 10x

Examples

72xe

4.277x ln 72x

Examples

3 2 42x

3.807x

ln 14ln 2x

Examples

2 52 3 4 11x

3.417x

35 1 log 7.52 2x

Examples

2 3 2 0x xe e

ln 2 and 0x x

Examples

5 5log 5 1 log 7x x

2x

Examples

52 log 3 4x

253x

Examples

10 10log 5 log 1 2x x

HO WEVER ......only works when you plugboth values back in to the original pro

5blem.

5 and -4x x

ha ha ha ha.....

A word problem example

rtA Pe

You found a bag full of money while coming out of Greenberry’s on the Green. You find $1575 in fives and tens in the bag and decide to put it in the bank at 5.35% interest compounded continuously and wait until the money doubles…that way you can return the original amount and no-one will be the wiser. How long will you have to wait for that to happen?

0.05 3515 75 tA e 0.05 35315 0 15 75 te 0.05 352 te

0.05 35ln 2 ln teln 2 0 .05 35 t

ln 2

0 .05 35t

12 .95 yearst

Go! Do!

Pre-Cal